*For correspondence:
stefan.klumpp@phys.uni-
goettingen.de (SK);
damien.faivre@cea.fr (DF)
†These authors contributed
equally to this work
Competing interests: The
authors declare that no
competing interests exist.
Funding: See page 12
Received: 09 April 2019
Accepted: 27 January 2020
Published: 28 January 2020
Reviewing editor: Raymond E
Goldstein, University of
Cambridge, United Kingdom
Copyright Bente et al. This
article is distributed under the
terms of the Creative Commons
Attribution License, which
permits unrestricted use and
redistribution provided that the
original author and source are
credited.
High-speed motility originates from
cooperatively pushing and pulling flagella
bundles in bilophotrichous bacteria
Klaas Bente1†, Sarah Mohammadinejad2,3,4†, Mohammad Avalin Charsooghi1,5,
Felix Bachmann1, Agnese Codutti1,2, Christopher T Lefe`vre6, Stefan Klumpp4*,
Damien Faivre1,6*
1Department of Biomaterials, Max Planck Institute of Colloids and Interfaces,
Potsdam, Germany; 2Department of Theory and Bio-Systems, Max Planck Institute
of Colloids and Interfaces, Potsdam, Germany; 3Department of Biological Sciences,
Institute for Advanced Studies in Basic Sciences, Zanjan, Islamic Republic of Iran;
4Institute for the Dynamics of Complex Systems, University of Go¨ttingen,
Go¨ttingen, Germany; 5Department of Physics, Institute for Advanced Studies in
Basic Sciences, Zanjan, Islamic Republic of Iran; 6Aix-Marseille Universite´, CEA,
CNRS, BIAM, F-13108, Saint-Paul-lez-Durance, France
Abstract Bacteria propel and change direction by rotating long, helical filaments, called flagella.
The number of flagella, their arrangement on the cell body and their sense of rotation
hypothetically determine the locomotion characteristics of a species. The movement of the most
rapid microorganisms has in particular remained unexplored because of additional experimental
limitations. We show that magnetotactic cocci with two flagella bundles on one pole swim faster
than 500 mms 1 along a double helical path, making them one of the fastest natural
microswimmers. We additionally reveal that the cells reorient in less than 5 ms, an order of
magnitude faster than reported so far for any other bacteria. Using hydrodynamic modeling, we
demonstrate that a mode where a pushing and a pulling bundle cooperate is the only possibility to
enable both helical tracks and fast reorientations. The advantage of sheathed flagella bundles is the
high rigidity, making high swimming speeds possible.
Introduction
The understanding of microswimmer motility has implications ranging from the comprehension of
phytoplankton migration to the autonomously acting microbots in medical scenarios
(Sengupta et al., 2017; Felfoul et al., 2016). The most present microswimmers in our daily lives are
bacteria, most of which use flagella for locomotion. Well-studied examples of swimming microorgan-
isms include the peritrichous (several flagella all over the body surface) Escherichia coli with an occa-
sionally distorted hydrodynamic flagella bundling (Turner et al., 2000) and the monotrichous (one
polar flagellum) Vibrio alginolyticus, which are pushed or pulled by a flagellum and exploit a
mechanical buckling instability to change direction (Xie et al., 2011; Son et al., 2013). The swim-
ming speeds of so far studied cells are in the range of several 10 mm s 1 and their reorientation
events occur on the time scale of 50–100 ms (Son et al., 2013; Berg and Brown, 1972).
Magnetococcus marinus (MC-1) is a magnetotactic, spherical bacterium that is capable of swim-
ming extremely fast (Zhang et al., 2014; Fenchel and Thar, 2004; Bazylinski et al., 2013; Garcia-
Pichel, 1989). MC-1 as well as the closely related strain MO-1 (Ruan et al., 2012) are equipped with
two bundles of flagella on one hemisphere (bilophotrichous cells). The bacterium also features a
magnetosome chain, which imparts the cell with a magnetic moment (‘magnetotactic’ cell). They are
Bente et al. eLife 2020;9:e47551. DOI: https://doi.org/10.7554/eLife.47551 1 of 17
RESEARCH ARTICLE
assumed to swim with the cell body in front of both flagella bundles, which synchronously push the
cell forward (Zhang et al., 2014). This assumption leads to helical motion in the presence of a strong
magnetic field, which exerts a torque on the cell’s magnetic moment, as seen in hydrodynamic simu-
lations (Yang et al., 2012). In the absence of a magnetic field, this model predicts rather straight
trajectories.
Our observations disagree with the above-mentioned model, indicating that an understanding of
the physics of their swimming is still missing, even though proof of concept biomedical applications
of these bacteria have already emerged (Felfoul et al., 2016). Here, we confirm that MC-1 cells
reach speeds of over 500 mm s 1 (Figure 1D) and observe that the cells travel along a double helical
path, which has not been reported for bilophotrichous cells so far. In addition, we observed that this
rapid movement is complemented by an extremely fast reorientation ability (less than 5 ms). We con-
nect the flagella bundle architecture and the swimming mechanism by hydrodynamic simulations
and show that only a striking cooperative movement where one flagella bundle pushes while the
other pulls the cell explains these motility characteristics.
Results
MC-1 cells were observed in a physicochemically controlled environment that resembled the cell’s
natural habitat (Adler, 1973; Figure 1A). The cells were introduced into a flat, rectangular
Figure 1. 3D tracking in physiochemically controlled conditions. (A) MC-1 cells were transitioned into agar-free
medium, the solution was degassed to remove the oxygen and inserted into a microcapillary. Due to one open
and one closed end, an oxygen gradient formed and the cells accumulated near their preferred microoxic
conditions (the oxic-anoxic-interface, OAI). (B) The cells were observed near the band using 400 fps phase contrast
video microscopy with a spherical aberration, which causes interference patterns around the spherical swimmers.
These patterns can be correlated with patterns from silica beads of known height relative to the focal plane. (C) A
tracking algorithm enables high-throughput 3D tracking of the microswimmers (Taute et al., 2015). Colors
indicate different cells. (D) Individual tracks were analyzed and a clockwise helical travel path with a radius close to
the cell diameter was found as well as instantaneous traveling speeds between 100 mm s 1 and 500 mm s 1. Tracks
can be interrupted by rapid reorientation events that last only 2.5–5 ms. The helix parameters like pitch and period
time do not change before and after an event, but apparently do so in the projected 2D tracks (see projected
shadow in D).
The online version of this article includes the following figure supplement(s) for figure 1:
Figure supplement 1. Validation of event identification algorithm for 3D tracking on simulated tracks with known
parameters.
Figure supplement 2. MC-1 swimming statistics.
Figure supplement 3. Oblique and top view of a typical event in an MC-1 swimming track.
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Research article Physics of Living Systems
microcapillary tube with a height of 200 mm, where they accumulated in a band near their preferred
oxygen conditions. The cells were imaged near this band (Frankel et al., 1997; Fenchel, 1994) at
central height to avoid surface interactions. The capillary was placed at the center of three orthogo-
nal Helmholtz coils (Bennet et al., 2014), which were used to cancel the Earth’s magnetic field with
a precision of 0.2 mT after the band had formed. Hence, the cells’ motion could be observed in the
absence of significant magnetic torques. Tracking was performed in 3D at 400 frames s 1 (fps)
(Figure 1B). A high-throughput tracking method was used (Taute et al., 2015) (see
Materials and methods) for the reconstruction of the tracks (Figure 1C and D).
Our first set of observations revealed that the cells traveled on helical paths (with a pitch of 5.3
mm ± 1.3 mm, a diameter of 1.7 mm ± 0.2 mm, and a period of 46 ms ± 32 ms, n = 65, errors are stan-
dard deviations) in the absence of magnetic torques (parameter extraction was performed with an
automated track analysis algorithm, which was validated against simulated swim tracks, see Fig-
ure 1—figure supplement 1 and Figure 1—figure supplement 2). In addition, abrupt changes of
the direction of the helical axis were observed (e.g. around 90˚ in Figure 1—figure supplement 3).
These directional changes occur within 2.5 ms to 5 ms, at least one order of magnitude faster than
any previously analyzed reorientation events (Son et al., 2013; Berg and Brown, 1972). Directional
changes did not occur via a continuous modulation of the ratio of radius and pitch (Crenshaw and
Edelstein-Keshet, 1993), as it has been observed as a part of the chemotaxis of sperm (Jikeli et al.,
2015). Rather, the helix parameters were the same before and after such an event. 3D tracking is
essential to obtain this conclusion, as projected 2D tracks exhibit apparent changes in the helix
parameters (see projected shadow of the track in Figure 1D and Figure 1—figure supplement 3).
The cells were further examined at 1640 fps in high-intensity dark-field video microscopy to visu-
alize the cell body and the flagella bundle movement in detail (Figure 2, Materials and methods). A
representative track of the cell body movement is shown in Figure 2A together with the tracked
velocity. At such frame rates, a more complex movement pattern becomes apparent, which was not
detectable during the 3D tracking at 400 fps. The cell track can be represented by a superposition
of two helices, a small helix on a large helix (Figure 2B), resulting in a position over time
Figure 2. High-speed dark-field video microscopy at 1640 fps reveals a dual helical travel path of a MC-1 cell
during free swimming. In (A) the tracked path is displayed after smoothing by a 5-point moving average filter and
then plotted together with the cell velocity. Green arrows indicate velocity maxima. In (B) it is shown that the
projected swimming path and projected velocity can be described by a projection of a large 3D double helix vd tð Þ.
Bente et al. eLife 2020;9:e47551. DOI: https://doi.org/10.7554/eLife.47551 3 of 17
Research article Physics of Living Systems
xd tð Þ ¼ rl cos
2pt
Tl
þ rs cos
2pt
Ts
; rl sin
2pt
Tl
þ rs sin
2pt
Ts
;
pl t
Tl
h i0
. The large helical track featured a pitch pl of ~4
mm, a radius rl of ~1 mm and a period Tl of 72 ms. The small helix featured a pitch of ~0.66 mm, a
radius rs of ~0.125 mm and a period Ts close to 14.4 ms. The ratio between this specific track’s
period times was close to 6, which was later used to choose the flagella bundle’s rigidities and tor-
que in the numerical simulations. The parameters for the small helix have been determined for a sin-
gle track and do not possess statistical information. However, comparable double helical paths were
apparent in all recorded tracks, including the cell track of the flagella imaging attempt (Figure 4,
Video 1 and Video 2).
The flagella bundle morphology and movements were imaged in transmission electron micros-
copy (TEM) and in high-intensity dark-field video microscopy (Figure 3, Video 1 and Video 2). In
the video microscopy at 1424 fps, short fibers next to the cell body and bright spots on the cell sur-
face could be observed, which we identified as a part of a flagellum bundle close to the cell surface
(Son et al., 2013). Although a state-of-the-art flagella imaging method, a sufficiently high framerate
and a photon density close to the cell death limit were chosen, the resulting images reveal only little
information about the exact flagella bundle positions and dynamics. This is the result of the combi-
nation of the small size of the cells and their extraordinary high swimming speed and possibly their
strong flagella bundle movement.
Despite the difficulties in imaging the flagella bundles in full length, the position of the flagella
bundle near the cell surface were tracked together with the cell’s trajectory over 85 ms, which corre-
sponds to 1.6 periods on the large helical trajectory of the cell (Figure 4). The observed movement
pattern is more complex than previously assumed (Felfoul et al., 2016; Frankel et al., 1997;
Bazylinski et al., 2013; Waisbord et al., 2016). The two flagella bundle positions moved rapidly
around the cell. Crucially, one flagella bundle position is often seen in front of the cell (relative to its
swimming direction), contrary to the model of two pushing flagella bundles, which remain behind
the cell body. Additionally, the bright spots’ movement pattern featured the same periodicity as the
large helical swimming track of the cell (also compare Figure 3C and Figure 3D).
We turned to numerical simulations of the cell’s swimming behavior, to develop a deeper under-
standing of the mechanisms of propulsion and rapid reorientation and to compensate the missing
information from flagella bundle imaging. We performed Stokesian dynamics simulations
(Adhyapak and Stark, 2015) for a spherical cell body (1.3 mm in diameter) with two discretized heli-
cal filaments (4 mm long and 50 nm thick if not stated differently) representing the flagella bundles
(see Materials and methods for details). A large helical path of a microswimmer is produced from an
off-axis (relative to the swimming direction) tor-
que which continuously changes the direction of
the thrust force. In case of a bilophotrichous cell,
Video 1. Cell observation in a high-intensity dark-field
video microscopy experiments at 1424 fps and 60x
magnification with cell tracking.
https://elifesciences.org/articles/47551#video1
Video 2. Cell observation in a high-intensity dark-field
video microscopy experiments at 1424 fps and 60x
magnification with cell tracking and tracking of white
spots on the cell surface.
https://elifesciences.org/articles/47551#video2
Bente et al. eLife 2020;9:e47551. DOI: https://doi.org/10.7554/eLife.47551 4 of 17
Research article Physics of Living Systems
this requires a significant asymmetry in the propulsion force vectors of the two flagella bundles. Five
possible asymmetries in flagella bundle configuration were considered to produce this torque and
the resulting swimming paths were compared to experimental data (Figure 5). Three asymmetric
configurations were ruled out numerically, as they did not result in a significant match between simu-
lated and experimentally observed helix diameter, helix pitch and speed. These configurations are:
A difference in flagella bundle length (Figure 5—figure supplement 1), a difference in motor
strength (Table 1) and an asymmetry in the equilibrium angle of the two flagella bundles relative to
the cell surface (Shum, 2019) (see Appendix 1). Another scenario would be a periodic, time-depen-
dent movement of the flagella equilibrium angles relative to the cell surface (Nguyen and Graham,
2017). However, constant offsets in these angles already did not produce any significant matches
between experiment and simulation. This indicates that this scenario will also fail this test and was
not investigated further. Although not fully reaching experimentally observed helix pitches, the
asymmetry in sense of motor rotation was the only scenario producing significant matches in helix
diameter and cell speeds.
Since TEM images did not allow for a precise determination of the opening angle between the
two flagella bundles (with respect to the body center; see, for example, Figure 3A), a wide range of
opening angles (30˚ 120˚) was used in the simulations (Figure 5—figure supplement 2). The effect
of the flagellar motors was included as a torque at the base of the helices, which rotates the fila-
ment, and a counter-torque, which rotates the cell body. We considered the two bundles to rotate
independently either counter-clockwise (CCW) or clockwise (CW). The parameters for bending rigid-
ity, torsion rigidity and torque of the flagella bundles were adjusted to reproduce the observed
movement characteristics (i.e. the parameters of the small helices and velocities). A motor torque of
12 pN mm, about 3.5 times the motor torque of an E. coli cell, had to be chosen together with high
isotropic bending and twisting rigidities of 7 pN mm2, about two times larger than for single flagella
(Adhyapak and Stark, 2015). We assume that this increase is attributed to the structure of the fla-
gella bundle, where seven protein motors power seven sheathed flagella cooperatively (Figure 3A).
Only this assumption allowed for stable and high swimming velocities in the simulations, indicating
that the function of the flagella bundle is to combine high torques with high rigidities.
Different swimming scenarios arising from combinations of CW and CCW rotation of the two bun-
dles were simulated: both flagella bundles pushing the cell (CCW and CCW), both flagella bundles
pulling (CW and CW) and one flagellum pushing, one pulling (CCW and CW). The fact that flagella
can pull cells is well established (Son et al., 2013; Constantino et al., 2016) and our simulations
Figure 3. Flagella bundle imaging. (A) TEM image of an MC-1 cell stained with uranyl acetate. Two flagella
bundles emerge from the MC-1 cell body. Each bundle features seven flagella, which emerge from a cavity on the
cell surface. The individual flagella are bundled by a sheath (scale bar is 1 mm). (B-D) Individual frames from the
high-speed dark-field video microscopy experiment at different points in time (Video 1, scale bars 1 mm). Bright
spots appeared on the cell surface and next to the cell, which were identified as the parts of the flagella bundles
that were closest to the cell surface. As the cell swam downwards in the image (blue track), the flagella bundle
spots appeared in front of and behind the cell (relative to its overall movement direction). When comparing the
times of B and C, the abrupt change in position indicates that another flagella bundle moved into focus of the
microscope. When comparing C and D, it becomes apparent that the spots appear at nearly the same position on
the cell at nearly the same horizontal position in the helical movement pattern, indicating a periodic flagella
movement pattern that causes the helical track.
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Research article Physics of Living Systems
show that only the CCW and CW model results in the double-helical tracks experimentally observed
(Figure 4A and B, Figure 5—figure supplement 2, Video 3 and Video 4). Tracking the simulated
cells resulted in time traces of the velocity and the projected position that are strikingly similar to
the experimental ones (for a quantitative comparison, see Figure 5 and Figure 2A). We tested the
dependence of the trajectories on model parameters, in particular the opening angle and motor tor-
que (Table 2 and Table 3). Double helical trajectories were observed for flagellar opening angles in
the whole parameter range, with diameter and speed in agreement with the experiments (but no
fully quantitative agreement for the pitch of the large helix).
We also tracked the position of the flagella bundle positions in the simulations (by tracking the
first beads of each discretized flagellum). Both flagella bundles rotated with 100 Hz - 150 Hz and
one period of the rotation coincides with one period of the large helix in the cell’s trajectory. This
agrees with the flagella bundle movement in the experiments (Figure 4).
Figure 4. Positions of flagella bundles on the cell over 85 ms at 1424 fps. (A) The cell swam from top to bottom in
the field of view. Moving bright spots were identified as the parts of the flagella bundles that were closes to the
cell surface. The cell’s helical traveling path had a period time of 52 ms. (B) The positions were tracked over time
and are depicted relative to the center of the cell, represented by different spheres for different time intervals. (C)
The schematic of the cell’s large helical track is color-coded according to the different time intervals where the
flagella bundle parts were visible to highlight the periodicity of the flagella bundle movement.
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Research article Physics of Living Systems
Our model suggests a pushing flagella bundle together with a pulling flagella bundle rotating in
opposite senses. The experimentally observed rapid reorientation events that lasts between 2.5 ms
and 5 ms are most reasonably produced by a sharp change in the rotation of at least one flagella
bundle. We tested different scenarios (Figure 5—figure supplements 3–5) and found a transiently
synchronous rotations of the two flagella bundles to be the most likely process. We tested this by
changing the sense of rotation from CCW and CW to CCW and CCW for 4 ms in the simulations and
calculating the angle between the trajectory segments before starting and after finishing this tran-
sient CCW and CCW step (outtake in Video 5). This procedure indeed resulted in rapid reorienta-
tion with a change in direction by 80˚ ± 8˚ (Figure 4C), in agreement with the 94˚ ± 39˚ change seen
Figure 5. Simulations of MC-1 swimming dynamics with one pushing and one pulling flagellar bundle. The
principle cell and flagella bundle arrangement is shown in (A) at four distinct time points where the cell body
diverges strongly from the helix axis. (B) Shows the projected track of a simulated MC-1 with the flagellar opening
angle 60o together with the projected speed. The results are comparable to measured data from Figure 2A. (C)
Histogram of turning angles for the reorientation events seen in experiments and in simulations, where
reorientation results from periods of synchronous rotation. (D) Validation of the cooperative pushing and pulling
model in the presence of a strong magnetic field (3 mT). A third hyper-helix is observed in both experiment and
simulation.
The online version of this article includes the following figure supplement(s) for figure 5:
Figure supplement 1. Swimming path parameters from numerical simulations with an asymmetry in flagella
lengths compared to experimental values.
Figure supplement 2. Comparison of cell path parameters from experiments and the pushper-puller simulation
scenario.
Figure supplement 3. Reorientation angle histogram for the following transient flagella bundle configuration:
CCW and CWfi CCW and 0fi CCW and CW (the rotation of the puller flagella is stopped during reorientation).
Figure supplement 4. Reorientation angle histogram for the following transient flagella bundle
configuration: CCW and CWfi CCW and CCWfi CW and CCWfi CW and CWfi CCW and CW.
Figure supplement 5. Reorientation angle histogram for the following transient flagella bundle configuration:
CCW and CWfi CCW and CCWfi CW and CCWfi CCW and CCWfi CCW and CW.
Figure supplement 6. Simulations of different scenarios of MC-1 swimming with varying magnetic fields and
magnetic moment orientation.
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Research article Physics of Living Systems
in the experiments (errors are standard deviations). The standard deviation of the directional change
is small in our simulations, where only the runtime was varied, compared to the experimental value.
The mismatch likely arises from biological diversity in flagella lengths and opening angles, but also
due to shifts in local physiochemical conditions, which can for example influence the motor torque
(Son et al., 2013). A transient buckling deformation was observed in the simulated flagella bundles
during an event, which caused the fast reorientations.
To further validate our simulations, we predicted the cell’s swimming behavior at high magnetic
fields using our simulation without changing further parameters. The direction of the cell’s magnetic
moment was assumed to be perpendicular to the bisector of the two flagella bundle axes (further
scenarios can be found in Figure 5—figure supplement 6). The simulations showed an additional,
large hyper-helical movement pattern (with diameter Dsim ’ 3:9 mm and pitch Psim ’ 19:1 mm). The
same pattern could thereafter be found in experimental data with similar parameters (Dexp ’ 4:2 mm
and Pexp ’ 30 mm). Typical MC-1 hyper-helical trajectories from simulations and experiments are
shown in Figure 5D.
Discussion
Magnetococci are exceptional swimmers with respect to both their high speed and their reorienta-
tion swiftness. In addition, they are likely to make use of a previously unrecognized pattern of motion
of their flagella bundles, with one bundle pushing the cell body and the other pulling it. Key to
observing this pattern of motion was the 3D tracking of single cells in the absence of magnetic tor-
ques to observe the unexpected two-helix trajec-
tories, together with hydrodynamic simulations.
Table 1. Simulated swim track parameters for an asymmetry in motor torques for MC-1 cells for
different opening angles between the two flagella bundles.
The second row gives statistical averages of experimental values for diameter (D), pitch (P), period
time (T) and speed (Vt).
Opening angle Tm2/Tm1 D (mm) P (mm) T (ms) Vt (mm/s)
Experiment 1.7 5.3 46.0 100.0
60 ˚ 0.1 0.43 0.93 47.4 52.33
0.5 0.29 0.73 20.2 58.85
0.9 0.18 1.58 33.4 88.42
80 ˚ 0.1 0.54 1.08 54.4 54.76
0.5 0.39 1.09 32 60.44
0.9 0.20 1.61 34.8 84.14
Video 3. Simulation of cell swimming with two pushing
flagella.
https://elifesciences.org/articles/47551#video3
Video 4. Simulation of cell swimming with one pulling
and one pushing flagella.
https://elifesciences.org/articles/47551#video4
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Research article Physics of Living Systems
The hierarchically organized flagella bundles provide a high torque and rigidity, necessary to reach
record speeds of over 200 body lengths per second, while the unusual type of coordination of the
two bundles provides a mechanism for rapid reorientation. Magnetotactic cocci such as MC-1 thrive
and generally represent the most abundant MTB in aquatic environments (Lefe`vre et al., 2015).
Their unusual motility is certainly an adaptation that represents a selective advantage that make
them competitive in the highly coveted biotopes that are the oxic-anoxic interfaces (Brune et al.,
2000). Indeed, the observed geometry of this resulting swimming pattern is reminiscent of the situa-
tion recently reported for magnetospirilla (Murat et al., 2015), despite the difference in body plan.
The magnetosprilla have two flagella at opposite cell poles, and a magnetic moment parallel to the
flagellar axis, while the flagella of the cocci studied here are attached on one hemisphere of the cell
and almost perpendicular to the magnetic moment. Nevertheless, both swim aligned with a mag-
netic field with one flagellum ahead and one trailing. In summary, record-breaking cells like MC-1
can help to understand physical limits of natural microswimmers and provide design principles for
their artificial counterparts.
Materials and methods
Key resources table
Reagent type (species) or resource Designation Source or reference Identifiers Additional information
Cell line (Magnetococcus marinus) MC-1 CEA NCBI:txid156889 Dr. Christopher Lefe`vre,
CNRS
Software, algorithm ImageJ NIH RRID:SCR_003070
Software, algorithm MatLab The MathWorks RRID:SCR_001622
Cell medium and culturing
MC-1 was cultured similarly to the procedure reported by Bazylinski et al. (2013). Artificial sea
water (ASW) was used as a base medium, containing 20 g NaCl, 6 g MgCl2, 2.4 g Na2SO4, 0.5 g KCl
and 1 g CaCl2 per liter H20. To this was added (per liter) the following, in order, prior to autoclaving:
0.05 mL 0.2% (w/w) aqueous resazurin, 5 mL Wolfe’s mineral solution (ATCC, MD-TMS), 0.3 g
NH4Cl, 2.4 g HEPES and 1.6 g agar (Kobe I, Carl Roth). The medium was then adjusted to pH 6.3
and autoclaved. After the medium had cooled to about 45˚C, the following solutions were added
(per liter), in order, from previously sterile-filtered stock solutions: 0.5 ml vitamin solution (ATCC,
MD-VS-10mL), 1.8 mL 0.5 M potassium phosphate buffer, pH 7, 3 mL0.01 M FeCl2 and 40% (w/w)
Na thiosulfate. Finally, 0.4 g cysteine was added (per liter), which was made fresh and filter-sterilized
indirectly into the medium. The medium (12 mL) was dispensed into sterile Hungate tubes after veri-
fying a pH of 7.0. All cultures were incubated at room temperature (~25˚C) and, after approximately
one week, a microaerobic band of MC-1 formed at the oxic–anoxic interface (pink-colorless inter-
face) of the tubes. The cells were harvested in volumes of 1 mL from that region and magnetically
transferred to ASW for experiments. The transfer step was necessary to remove agar for swimming
experiments and to minimize background scattering in dark-field microscopy.
Cell morphology analysis
The flagella bundle length was determined with ImageJ from images taken with a Zeiss EM 912
Omega transmission electron microscope using an acceleration voltage of 120 kV. The cells were
dried on a carbon film on a regular TEM copper grid and stained with 4% uranyl acetate for 6 min.
Due to the staining, the cell walls appeared electron dense and covered the sight on flagella on top
or below the cells. Hence, we added the average cell radius to the mean of the flagella length. A
mean flagella bundle length of 3.3 mm ± 0.4 mm (n = 27) resulted. The size of the non-dried cells
were measured with ImageJ from images taken with a LSM780 (Zeiss; Germany) confocal micro-
scope. The mean size was 1.3 mm ± 0.1 mm (n = 103).
Microcapillary experiments
1 mL of a freshly harvested sample was degassed using nitrogen for 15 min and the sample was
introduced into a rectangular micro-capillary (VitroTubes, #3520–050,) by capillary forces. One end
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Research article Physics of Living Systems
of the capillary was sealed with petroleum jelly and the capillary was mounted on a microscope slide
that was used to hold the sample on the microscope stage. The oxygen diffusion from the open end
caused an oxygen gradient inside the medium, which led together with the oxygen consumption of
the cells to the formation of a microaerobic bacteria band. The band formed in the presence of a 50
mT magnetic field towards the sealed end. The tracks were taken after 30 min of microcapillary infil-
tration at 0 mT.
3d tracking experiments
3D swim tracks were recorded at 400 fps in a microcapillary in the vicinity of the microaerobic band
(Nikon, S Plan Fluor ELWD,40, Ph2, NA 0.6; NA 0.76 condenser lens; Ph2 aperture ring, 635 nm
LED illumination). The 3D tracks were reconstructed using the high-throughput phase contrast refer-
ence method by Taute et al. (2015). A spherical aberration was introduced using a misalignment of
the correction collar of the 40 phase contrast objective to a cover slip thickness correction of 1.2
mm. The aberration caused inference pattern, which can be correlated with the relative height of the
microswimmer. A custom made microscope platform, developed by Bennet et al. (2014), was used,
which features three orthogonal Helmholtz coil pairs around the sample position. The setup can gen-
erate homogeneous fields at the sample position with arbitrary direction with a precision of 0.2 mT.
The Earth’s magnetic field was canceled or an artificial field towards low oxygen conditions was gen-
erated during a capillary experiments.
Dark-field microscopy
Flagella bundle positions were visualized at 1424 fps using high-intensity dark-field microscopy
(Nikon 60, 0.5–1.25 NA CFI P-Fluor oil objective at 0.75 NA; 1.2 NA oil condenser; mercury lamp
illumination) and an Andor Zyla 5.5 (10-tap) camera (6.5 mm per pixel). The cells were placed inside a
10 mm deep chamber in ASW. A deeper chamber did not allow for successful dark-field imaging of
flagella bundles due to an increase in noise from background scattering. The focal plane was
adjusted to the center of the chamber, such that interactions between the observed flagella bundles
and the chamber surfaces were avoided. Presumably due to the flagella bundle size and the high
Table 2. Swimming features of MC-1 cells using CCW and CW swimming mechanism for simulations with different flagellar opening
angles.
The given output parameters are the helix diameter, its pitch, the period time (period), the effective velocity (Vz) and the instantaneous
velocity (Vt).
Flagellar opening angle Diameter (mm) Pitch (mm) Period (ms) Vz (mm/s) Vt (mm/s)
30˚ 2.1 3.0 144 21 76
45˚ 1.7 2.3 88 27 87
60˚ 1.4 1.7 59 30 96
80˚ 1.1 1.2 39 32 106
100˚ 0.9 1.1 34 32 108
120˚ 0.7 1.1 34 33 106
Table 3. Swimming features of MC-1 cells for different motor torques.
The 3.5 times increase of motor torque compared to E-coli cells was chosen for the simulations
described in the main text due to the best fits of swimming track parameters.
Motor torque (Tm/Tm-Ecoli) D (mm) P (mm) T (ms) Vt (mm/s)
3.5 1.4 1.7 59 96
3 1.44 1.56 74.4 80.84
2.5 1.43 1.64 84.2 69.41
2 1.49 1.39 101.2 53.27
Bente et al. eLife 2020;9:e47551. DOI: https://doi.org/10.7554/eLife.47551 10 of 17
Research article Physics of Living Systems
rotation speed of the cell and of the bundles, a
direct observation of the whole flagella bundles
was not successful and only a small section of
each flagellum could be visualized. A sub-milli-
second exposure time set the requirement for
high photon intensity at the sample position.
The intensity was increased until the cells melted
instantly when swimming into focus. A green fil-
ter prevented the melting while still facilitating
sufficient brightness. Scrupulous cleanliness at all
optical interfaces was obligatory. High-speed
cell body tracking could be accomplished at the
center of a 200 mm deep chamber. Optimized
visualization was achieved at 1640 fps using
dark-field microscopy without the critical illumi-
nation from flagella tracking (Zeiss 60, 1.0 NA;
1.2 NA oil condenser; halogen lamp illumina-
tion). The dark-field setup did not allow for a cancellation of external magnetic fields. Measurements
of the magnetic field at the capillary position yielded Bx =  195 mT ± 0.2 mT, By = 60 mT ± 0.2 mT
and Bz = 27 mT ± 0.2 mT.
Cell and flagella tracking software
3D track reconstruction was performed in MatLab (The MathWorks) using an adapted version of the
code from Taute et al. (2015). For automated analysis of the reorientation angle distribution, the
script was successfully tested against simulated data with known reorientation angles (See SI). The
helix parameter determination was performed automatically on tracks extending a duration of 0.4 s,
with a mean-square-displacement of at least 10 mm2 and a mean opening angle between all conse-
cutive velocity vectors of less than 60 ˚ to exclude strongly irregular tracks. The same exclusion
parameters have been used for the reorientation angle analysis. Simultaneous dark-field cell and fla-
gella tracking was performed using an in-house semi-automatic MatLab program. Tracking of the
cell trajectory at 1640 fps without the flagella movement was performed using the TrackMate plugin
of ImageJ.
Hydrodynamic simulations
Each flagellum was modeled as a helical filament and a rotary motor. The helical filament was discre-
tized with 20 beads with a discretization distance of 200 nm and bead diameter of 50 nm. Excluded
volume interactions between all particles are considered using a truncated Lennard-Jones potential.
Hydrodynamic interactions are taking into account using Stokesian dynamics simulation method hav-
ing the translational anisotropic friction coefficients of gNoentity ¼ 1:6  10
 3 pNs/mm2 and
g? ¼ 2:8 10
 3 pNs/mm2 and the rotational friction of gr ¼ 1:26 10
 6 pNs for the flagellum beads
and gbt ¼ 6phRb and gbr ¼ 8phR
3
b for the translational and rotational friction coefficients of the cell
body. Irrespective of the high motor torque and isotropic bending and twisting rigidities mentioned
in the main text, a stretching rigidity of 1000 pN, comparable to that of single flagella, could be cho-
sen. A Rotne-Prager matrix was used for calculating the cross-mobilities and cross-hydrodynamics
(Dhont, 1996). The swimming dynamics of the model cell at low Reynold number was calculated by
solving the translational and rotational Stokes equations of motion for the cell body, flagellar beads
and the bonds between them. A second-order Runge-Kutta algorithm (Sewell, 1988; Press et al.,
1992) and simulation time-steps of 10 7 s were used to solve the equations of motion numerically.
Acknowledgements
The research leading to these results was supported by the Max Planck Society and by Deutsche
Forschungsgemeinschaft (DFG) within the priority program on microswimmers (grants No. KL 818/2–
2 and FA 835/7–2 to SK and DF). Further, SM was supported by Deutscher Akademischer Austausch-
dienst, DAAD (grant no. 57314018) as well as Deutsche Forschungsgemeinschaft (DFG) through SFB
Video 5. Example simulation of reorientation events.
https://elifesciences.org/articles/47551#video5
Bente et al. eLife 2020;9:e47551. DOI: https://doi.org/10.7554/eLife.47551 11 of 17
Research article Physics of Living Systems
937. AC is funded by the IMPRS on Multiscale Biosystems. CTL acknowledges support by the French
National Research Agency (ANR Tremplin-ERC: ANR-16-TERC-0025–01). The authors would further
like to thank L Alvarez, R Pascal and J Jikeli for measurement trainings, C Oschatz for medium prep-
aration, A Pohl for electron microscopy and C Pilz for laboratory assistance.
Additional information
Funding
Funder Grant reference number Author
Max-Planck-Gesellschaft Damien Faivre
Deutsche Forschungsge-
meinschaft
FA 835/7-2 Damien Faivre
Deutsche Forschungsge-
meinschaft
KL 818/2-2 Stefan Klumpp
Deutscher Akademischer Aus-
tauschdienst
57314018 Sarah Mohammadinejad
Deutsche Forschungsge-
meinschaft
SFB 937 (A21) Stefan Klumpp
Agence Nationale de la Re-
cherche
ANR-16-TERC-0025-01 Christopher T Lefe`vre
IMPRS on Multiscale Biosys-
tems
Agnese Codutti
French National Research
Agency
ANR Tremplin-ERC: ANR-
16-TERC-0025-01
Christopher T Lefe`vre
The funders had no role in study design, data collection and interpretation, or the
decision to submit the work for publication.
Author contributions
Klaas Bente, Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation,
Visualization, Methodology; Sarah Mohammadinejad, Data curation, Software, Formal analysis, Vali-
dation, Investigation, Visualization, Methodology; Mohammad Avalin Charsooghi, Software, Valida-
tion, Investigation, Visualization; Felix Bachmann, Software, Methodology; Agnese Codutti,
Software, Validation, Methodology; Christopher T Lefe`vre, Resources, Supervision, Methodology;
Stefan Klumpp, Conceptualization, Resources, Formal analysis, Supervision, Funding acquisition,
Methodology; Damien Faivre, Conceptualization, Resources, Supervision, Funding acquisition, Vali-
dation, Project administration
Author ORCIDs
Klaas Bente https://orcid.org/0000-0002-2520-4697
Sarah Mohammadinejad https://orcid.org/0000-0002-3758-5693
Mohammad Avalin Charsooghi https://orcid.org/0000-0002-7772-8513
Stefan Klumpp https://orcid.org/0000-0003-0584-2146
Damien Faivre https://orcid.org/0000-0001-6191-3389
Decision letter and Author response
Decision letter https://doi.org/10.7554/eLife.47551.sa1
Author response https://doi.org/10.7554/eLife.47551.sa2
Additional files
Supplementary files
. Transparent reporting form
Bente et al. eLife 2020;9:e47551. DOI: https://doi.org/10.7554/eLife.47551 12 of 17
Research article Physics of Living Systems
Data availability
3D tracks have been deposited in Dryad Digital Repository (https://doi.org/10.5061/dryad.r2nd550).
The following dataset was generated:
Author(s) Year Dataset title Dataset URL
Database and
Identifier
Bente K, Moham-
madinejad S, Char-
sooghi MA,
Bachmann F, Co-
dutti A, Lefe`vre CT,
Klumpp S, Faivre D
2019 Data from: High-speed motility
originates from cooperatively
pushing and pulling flagella
bundles in bilophotrichous bacteria
https://doi.org/10.5061/
dryad.r2nd550
Dryad Digital
Repository, 10.5061/
dryad.r2nd550
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Appendix 1
Supplementary Information
Rapid change in swimming direction
An exemplary track of a fast reorientation event is given in Figure 1—figure supplement 3. A
change in swimming direction by roughly 90 ˚ occurred in less than 5 ms.
3D tracking validation
The algorithm for 3D track event detection was validated using Langevin-simulations of active
Brownian particles with defined mean reorientation angles, velocities, mean run times and
mean run lengths, as described in Figure 1—figure supplement 1. Two parameter sets have
been simulated and used for validation. The evaluation shows good agreement between input
and output parameters. The swim track parameters that have been determined from 3D tracks
of MC-1 cells in the capillary experiment are presented in Figure 1—figure supplement 2.
Relation between helical and effective travel path
The overall traveled path l on a helix during one period can be parameterized using radius and
pitch by l ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
p2 þ 4p2r2
p
¼ 7:5 m. While effectively traveling 4 mm in 72 ms, the cell moves 7.5
mm on the large helix. While the contribution of the small helix to the actual swimming path
provides another factor of 1.1, the ratio between instantaneous speed and effective speed is
near 2.
Test of different asymmetries in flagella configurations
1) Asymmetry in senses of rotation of motors
This asymmetry is described in the main text.
2) Asymmetry in flagella lengths
Simulations for different combinations of flagella lengths, L1 = 2, 3 mm, L2 = 4, 5, 6, 7, 8 mm
(with 2 opening angles 60, 80) were performed. With this asymmetry in flagella length, a
helical path can be observed but, as shown in Figure 5—figure supplement 1, the size of the
second helix isn’t comparable to the experimental values.
Moreover, the curves in Figure 5—figure supplement 1 are flat, indicating that changing
the strength of asymmetry doesn’t have remarkable effect on the size of the second helix.
3) Asymmetry in motor strengths
In these simulations the motor torque of one flagellum (Tm2) is 0.1, 0.5 or 0.9 times the torque
of the other flagellum (Tm1). We observed double-helical trajectory with this motor asymmetry
as well but with considerably smaller size compared to the experiment and our proposed
pusher-puller model. The size of helix and swimming features are presented in Table 1, as well
as experimental values for comparison.
Among these simulations the largest helix is observed for Tm2/Tm1 = 0.1 which is still
smaller than the size of the experimental helix. Moreover, a hypothetical multi-flagellated
microorganism that features flagella with a huge difference in motor torque (Tm2/Tm1 = 0.1)
it is biologically not relevant. Also, the simulated velocities did not fit the experimental values
for any of the tested scenarios.
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Research article Physics of Living Systems
4) Asymmetry in flagella direction
We performed simulations with asymmetry in flagella direction. For this purpose, combination
of flagella angles 0˚ and 10˚, 0˚ and 20˚, 0˚ and 30˚ and 0˚ and 40˚ as hinge equilibrium angles
have been tested. In swimming trajectories, a very weak second helix with diameters of about
an order of magnitude smaller than our pusher-puller model was observed.
For example, for 0˚ and 30˚ resulted in D = 0.17 mm, p=3.18 mm, Vt = 71.50 mm/s. Which is
far from the experimental ones: D = 1.7 mm, p=5.3 mm, Vt = 100.0 mm/s.
In these simulations, the more tilted flagella bundle is only tilted close to the cell surface,
but due to flexibility, the tilt is not persistence along the length of the flagella bundle and the
two bundles approach each other at their end parts. So, the results show that asymmetry in
flagella direction cannot generate a helix comparable to MC-1’s large helix.’
Discussion of pitch differences between simulation and
experimental observation
While the pitch of the simulation result, presented in the main text, is off by a factor of 2, the
diameter and period time of helical trajectories are in good agreement with the experiments.
The simulations show that the features of helical trajectories strongly depend on the flagellar
opening angle (see Table 2) such that increasing the flagellar opening angle decreases the
pitch and diameter of the large helix. Simulated effective velocities are smaller than the
tracked velocities by factor of 2, since the pitch is decreased by the same factor while the
period times are comparable.
Since the simulations with constant flagella length did not lead to a satisfying match in
pitches, further simulations for different combinations of opening angles and flagellum lengths
were carried out. The resulted diameter, pitch and velocity are compared with experimental
values in Figure 5—figure supplement 2.
From these simulations, we can conclude that there are some other combinations of
opening angle and flagellum length (for example L = 5 mm, opening angle = 60˚) with which
we can achieve a similar qualitative matching between simulation and experiment. However,
none of them satisfy all the parameters simultaneously. The best match between helix
diameter, pitch and speed is described in the main text. However, we clarify here that other
tuning parameters (for example flagellum length and diameter, flagella opening angle, the
motor torque) in the model cannot be precisely determined from TEM or optical microscopy
images of MC-1. Therefore, it is computationally very time consuming to test different values
for all these tuning parameters to find an accurate quantitative match for all parameters
between experiment and simulation.
We further investigated several motor torques. Due to the collapse of our simulation for
strong motors (because of the arising numerical error), the maximum applicable torque was 12
pN mm (about 3.5 times the motor torque of an E. coli). However, we can extrapolate the
swimming behavior of our model MC-1 at higher motor torques by looking at its trend for
lower values of motor torque. We tried motor torques of 2, 2.5, 3, and 3.5 times the motor
torque ofE. coliand the results are listed in Table 3.
The top row represents the result discussed in the main text. The overall pitch increases
with increasing motor torque. It can be concluded that the motor torque can be one of the
parameters that may help matching between experiment and simulation, although the
definitive match was not reached in this study.
Transient flagella configurations that produce fast reorientation
events
Three possible transient flagella configurations for reorientation events were tested in the
simulations (CCW meaning counter-clockwise and CW meaning clockwise).
1. CCW and CW fi CCW and 0 fi CCW and CW (the rotation of the puller flagella is stopped
during reorientation). An average reorientation angle of 25˚ resulted.
Bente et al. eLife 2020;9:e47551. DOI: https://doi.org/10.7554/eLife.47551 16 of 17
Research article Physics of Living Systems
2. CCW and CW fi CCW and CCW fi CW and CCW fi CW and CW fi CCW and CW. The
average reorientation angle for this transient configuration change was 105˚.
3. CCW and CW fi CCW and CCW fi CW and CCW fi CCW and CCW fi CCW and CW. The
average reorientation angle for this transient configuration change was 105˚.
Based on these results, we concluded that the reorientation angle statics produced by
CCW and CWfi CCW and CCWfi CCW and CW matched the best to the experiment result.
Flagella bundle morphology
The MC-1 cell shape is given in Figure 3A in the main text, where seven individual flagella
were identified, emerging from a sunken pit, as already described in Bazylinski et al. (2013).
The individual bundles of the close relative MO-1 (Ruan et al., 2012) contain seven individual
flagella, as well, which emerge from a hexagonal pattern on the cell surface. Additionally, 24
gap-filling, presumably friction-reducing microfibrils were found in Ruan et al. (2012). We
assumed a similar flagella arrangement in this study, leading to a cooperative torque
generation of the individual flagella in one sheath of an MC-1 cell.
Test of different motor torque, magnetic moment direction and
magnetic field configurations
To check for the validity of simulation prediction, an experiment is set up in low and high
magnetic fields, 50 T and 3 mT, respectively. Over 1000 tracks are extracted and
investigated for each magnetic field. For more certainty, swimming trajectories are
investigated both in oxic and anoxic regions. In high magnetic field, over 80 trajectories can
be detected illustrating the hyper-helix, while in Earth magnetic field only a few trajectories
with semi-hyper-helix can be observed. A typical MC-1 trajectory with the mentioned hyper-
helix resulted from simulation and experiment is shown in Figure 4D. A measured diameter
and pitch of the hyper-helix, Dexp ’ 4:2m and Pexp ’ 30m, are in reasonable agreement with
the simulated one, Dsim ’ 3:9m and Psim ’ 19:1m.
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Research article Physics of Living Systems